%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO219^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:07:51 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 57 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 88 ( 27 ~; 0 |; 0 &; 58 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 58 ( 2 ^; 44 !; 12 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cS,type,
cS: $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i > $i > $i ).
thf(tp_sK2_SY6,type,
sK2_SY6: ( $i > $i ) > $i ).
thf(tp_sK3_E,type,
sK3_E: ( $i > $i > $i ) > $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $i ) > $i > ( $i > $i > $i ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $i ) > ( $i > $i ) > $i > ( $i > $i > $i > $i ) > $i ).
thf(1,conjecture,
( ! [M: $i] :
( ( cS @ M )
!= M )
=> ~ ? [G: $i > $i > $i] :
! [F: $i > $i] :
? [J: $i] :
( ( G @ J )
= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM6) ).
thf(2,negated_conjecture,
( ( ! [M: $i] :
( ( cS @ M )
!= M )
=> ~ ? [G: $i > $i > $i] :
! [F: $i > $i] :
? [J: $i] :
( ( G @ J )
= F ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [M: $i] :
( ( cS @ M )
!= M )
=> ~ ? [G: $i > $i > $i] :
! [F: $i > $i] :
? [J: $i] :
( ( G @ J )
= F ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [M: $i] :
( ( cS @ M )
!= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ? [G: $i > $i > $i] :
! [F: $i > $i] :
? [J: $i] :
( ( G @ J )
= F ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ? [G: $i > $i > $i] :
! [F: $i > $i] :
? [J: $i] :
( ( G @ J )
= F ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [M: $i] :
( ( cS @ M )
!= M ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ? [G: $i > $i > $i] :
! [F: $i > $i] :
? [J: $i] :
( ( G @ J )
= F ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i > $i > $i] :
~ ! [SX1: $i > $i] :
~ ! [SX2: $i] :
( ( SX0 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SX0: $i] :
( ( cS @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i > $i > $i] :
~ ! [SX1: $i > $i] :
~ ! [SX2: $i] :
( ( SX0 @ SX2 )
!= SX1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ( cS @ SV1 )
!= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SY4: $i > $i] :
~ ! [SY5: $i] :
( ( sK1_SX0 @ SY5 )
!= SY4 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ( cS @ SV1 )
= SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SY4: $i > $i] :
~ ! [SY5: $i] :
( ( sK1_SX0 @ SY5 )
!= SY4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
! [SV2: $i > $i] :
( ( ~ ! [SY6: $i] :
( ( sK1_SX0 @ SY6 )
!= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV2: $i > $i] :
( ( ! [SY6: $i] :
( ( sK1_SX0 @ SY6 )
!= SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV2: $i > $i] :
( ( ( sK1_SX0 @ ( sK2_SY6 @ SV2 ) )
!= SV2 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(19,plain,
! [SV2: $i > $i] :
( ( ( sK1_SX0 @ ( sK2_SY6 @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(20,plain,
! [SV2: $i > $i] :
( ( ! [SV3: $i] :
( ( sK1_SX0 @ ( sK2_SY6 @ SV2 ) @ SV3 )
= ( SV2 @ SV3 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV4: $i,SV2: $i > $i] :
( ( ( sK1_SX0 @ ( sK2_SY6 @ SV2 ) @ SV4 )
= ( SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV6: $i] :
( ( ( cS @ SV6 )
= SV6 )
= $false ),
inference(rename,[status(thm)],[14]) ).
thf(30,plain,
! [SV10: $i,SV11: $i > $i] :
( ( ( sK1_SX0 @ ( sK2_SY6 @ SV11 ) @ SV10 )
= ( SV11 @ SV10 ) )
= $true ),
inference(rename,[status(thm)],[22]) ).
thf(31,plain,
! [SV10: $i,SV11: $i > $i,SV6: $i] :
( ( ( ( sK1_SX0 @ ( sK2_SY6 @ SV11 ) @ SV10 )
= ( SV11 @ SV10 ) )
= ( ( cS @ SV6 )
= SV6 ) )
= $false ),
inference(res,[status(thm)],[30,24]) ).
thf(33,plain,
! [SV10: $i,SV14: $i > $i] :
( ( ( cS @ ( SV14 @ SV10 ) )
= ( cS
@ ( sK1_SX0
@ ( sK2_SY6
@ ^ [SX0: $i] : ( cS @ ( SV14 @ SX0 ) ) )
@ SV10 ) ) )
= $false ),
inference(extuni,[status(esa)],[31:[bind(SV6,$thf( sK1_SX0 @ ( sK2_SY6 @ ^ [SX0: $i] : ( cS @ ( SV14 @ SX0 ) ) ) @ SV10 )),bind(SV11,$thf( ^ [SX0: $i] : ( cS @ ( SV14 @ SX0 ) ) ))]]) ).
thf(53,plain,
! [SV47: $i,SV48: $i > $i] :
( ( ( cS @ ( SV48 @ SV47 ) )
= ( cS
@ ( sK1_SX0
@ ( sK2_SY6
@ ^ [SX0: $i] : ( cS @ ( SV48 @ SX0 ) ) )
@ SV47 ) ) )
= $false ),
inference(rename,[status(thm)],[33]) ).
thf(65,plain,
$false = $true,
inference(extuni,[status(esa)],[53:[bind(SV47,$thf( sK2_SY6 @ ^ [SX0: $i] : ( cS @ ( sK1_SX0 @ SX0 @ SX0 ) ) )),bind(SV48,$thf( ^ [SX0: $i] : ( sK1_SX0 @ SX0 @ SX0 ) ))]]) ).
thf(66,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO219^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n010.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 17:33:55 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25
% 0.07/0.25 No.of.Axioms: 0
% 0.07/0.25
% 0.07/0.25 Length.of.Defs: 0
% 0.07/0.25
% 0.07/0.25 Contains.Choice.Funs: false
% 0.07/0.25 .
% 0.07/0.25
% 0.07/0.25 ********************************
% 0.07/0.25 * All subproblems solved! *
% 0.07/0.25 ********************************
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:65,loop_count:8,foatp_calls:3,translation:fof_full)
% 0.07/0.25
% 0.07/0.25 %**** Beginning of derivation protocol ****
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 %**** End of derivation protocol ****
% 0.07/0.25 %**** no. of clauses in derivation: 28 ****
% 0.07/0.25 %**** clause counter: 65 ****
% 0.07/0.25
% 0.07/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:65,loop_count:8,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------